Optimal Graphs in the Enhanced Mesh Networks

The degree diameter problem explores the biggest graph (in terms of number of nodes) subject to some restrictions on the valency and the diameter of the graph. The restriction on the valency of the graph does not impose any condition on the number of edges (apart from taking the graph simple), so th...

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Main Authors:	Muhammad Shahzad Akhtar, Muhammad Imran, Syed Ahtsham ul Haq Bokhary
Format:	Article
Language:	English
Published:	Hindawi Limited 2020-01-01
Series:	Journal of Mathematics
Online Access:	http://dx.doi.org/10.1155/2020/9869201

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record_format	Article
spelling	doaj-f34e59a09d5c4ef5b4f6ad99a5d5de562020-11-25T02:58:54ZengHindawi LimitedJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/98692019869201Optimal Graphs in the Enhanced Mesh NetworksMuhammad Shahzad Akhtar0Muhammad Imran1Syed Ahtsham ul Haq Bokhary2Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakaria University, Multan, PakistanDepartment of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551 Al Ain, UAECenter for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakaria University, Multan, PakistanThe degree diameter problem explores the biggest graph (in terms of number of nodes) subject to some restrictions on the valency and the diameter of the graph. The restriction on the valency of the graph does not impose any condition on the number of edges (apart from taking the graph simple), so the resulting graph may be thought of as being embedded in the complete graph. In a generality of the said problem, the graph is taken to be embedded in any connected host graph. In this article, host graph is considered as the enhanced mesh network constructed from the grid network. This article provides some exact values for the said problem and also gives some bounds for the optimal graphs.http://dx.doi.org/10.1155/2020/9869201
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Muhammad Shahzad Akhtar Muhammad Imran Syed Ahtsham ul Haq Bokhary
spellingShingle	Muhammad Shahzad Akhtar Muhammad Imran Syed Ahtsham ul Haq Bokhary Optimal Graphs in the Enhanced Mesh Networks Journal of Mathematics
author_facet	Muhammad Shahzad Akhtar Muhammad Imran Syed Ahtsham ul Haq Bokhary
author_sort	Muhammad Shahzad Akhtar
title	Optimal Graphs in the Enhanced Mesh Networks
title_short	Optimal Graphs in the Enhanced Mesh Networks
title_full	Optimal Graphs in the Enhanced Mesh Networks
title_fullStr	Optimal Graphs in the Enhanced Mesh Networks
title_full_unstemmed	Optimal Graphs in the Enhanced Mesh Networks
title_sort	optimal graphs in the enhanced mesh networks
publisher	Hindawi Limited
series	Journal of Mathematics
issn	2314-4629 2314-4785
publishDate	2020-01-01
description	The degree diameter problem explores the biggest graph (in terms of number of nodes) subject to some restrictions on the valency and the diameter of the graph. The restriction on the valency of the graph does not impose any condition on the number of edges (apart from taking the graph simple), so the resulting graph may be thought of as being embedded in the complete graph. In a generality of the said problem, the graph is taken to be embedded in any connected host graph. In this article, host graph is considered as the enhanced mesh network constructed from the grid network. This article provides some exact values for the said problem and also gives some bounds for the optimal graphs.
url	http://dx.doi.org/10.1155/2020/9869201
work_keys_str_mv	AT muhammadshahzadakhtar optimalgraphsintheenhancedmeshnetworks AT muhammadimran optimalgraphsintheenhancedmeshnetworks AT syedahtshamulhaqbokhary optimalgraphsintheenhancedmeshnetworks
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Optimal Graphs in the Enhanced Mesh Networks

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